Cоnsider а binаry string representing аn integer between 0 and . Suppоse is initialized such that it cоnsists of all 1's and no 0's. Thus, is any integer that can be represented by a binary string of all 1's. Now consider the DECREMENT operation, that reduces the value of the number represents by exactly 1: Note that we assume the zeroth position of is the least significant bit of the string (farthest bit to the right), and the position is the most significant bit (farthest bit on the left). We wish to calculate the amortized cost of a DECREMENT operation if we are counting from down to 0. Using the accounting method only, prove that given calls to DECREMENT(), the amortized time cost of each DECREMENT operation is . (Note: Provide your answer in the space provided.)